How to find minimum force required to take a block up the inclined plane
The minimum force required to take the block up the incline will be equal to the component of its weight along the incline. When the equal force is applied it will move up with a constant velocity.
Now soppose the incline makes angle a with the horizontal the component of the weight along the incline is mgsin a
So the minimum force is when no net acceleration happens that is when we apply force mgsin a .